A compact high order finite volume scheme for advection-diffusion-reaction equations

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Abstract

We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying Gauss-Legendre quadrature rules to the integral representation gives the high order finite volume complete flux scheme, which is fourth order accurate for both diffusion dominated and advection dominated flow.
Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics (Proceedings ICNAAM 2009, Rethymno, Crete, Greece, September 18-22, 2009)
EditorsT.E. Simos, G. Psihoyios, C. Tsitouras
Place of PublicationMelville NY
PublisherAmerican Institute of Physics
Pages410-414
ISBN (Print)978-0-7354-0705-3
DOIs
Publication statusPublished - 2009

Publication series

NameAIP Conference Proceedings
Volume1168
ISSN (Print)0094-243X

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    Anthonissen, M. J. H., & Thije Boonkkamp, ten, J. H. M. (2009). A compact high order finite volume scheme for advection-diffusion-reaction equations. In T. E. Simos, G. Psihoyios, & C. Tsitouras (Eds.), Numerical Analysis and Applied Mathematics (Proceedings ICNAAM 2009, Rethymno, Crete, Greece, September 18-22, 2009) (pp. 410-414). (AIP Conference Proceedings; Vol. 1168). Melville NY: American Institute of Physics. https://doi.org/10.1063/1.3241484